Bed frames and other types of support structures are used to elevate and support mattress foundations (box springs) and mattresses, together sometimes referred to as “sleep sets”. Bed frames and other elevating support structures have traditionally been constructed of wood or steel, and have perimeter members or frame rails which fit with the perimeter of the foundation, cross members which extend between the perimeter members, and vertical legs which elevate and support the frame members. Bed frames are preferably adjustable, in width, length and elevation (vertical extent of the legs). In any particular adjusted size, the frame must be rigidly secured and adequately supported by the legs for safe weight-bearing performance. When made of steel, the frame members must be fastened together very tightly to make the frame stiff and noise free. Although the bed frame legs are typically located proximate to the ends of the frame rail members, in many installations the frame rails may extend substantially beyond the closest supporting leg, longitudinally or transversely, and there may be substantial lengths between legs. Also, two or more frame rails may be aligned to form a long run of the frame, particularly in a transverse or width-wise direction of the frame, i.e., between longitudinal members of the frame. In this type of installation, adjoining ends of the frame rails must be secured together in order to allow for adjustment of the frame width. It is also desirable to have a supporting leg located at the adjoining or overlapping ends of aligned frame rails, and is often required when the frame width is increased.